The Wisconsin-based department store chain has quietly been working on an alliance with the e-commerce giant since the spring, Kohl's chief merchandising and customer officer, Michelle Gass, told CNBC.

"I really do think it's an example of two companies that can leverage each other's strengths," said Gass, who will take the retailer's chief executive position, succeeding Kevin Mansell, in May. Gass has been spearheading Kohl's partnership with Amazon.

"We're leaning into our store base, which is a competitive advantage for us," she added.

The kiosks selling Amazon products, such as the Echo or the Kindle, in Kohl's stores will be run entirely by Amazon, Gass explained. But for the returns process, Kohl's own employees will be doing the work. More than 70 additional stores will eventually be able to process Amazon returns, though Kohl's won't say if those launches will come ahead of the holidays.

Source: Kohl's

The Amazon kiosk in a Kohl's department store.

Amazon working with Kohl's just makes sense, according to Tiffany Hogan, an apparel analyst at Kantar Retail.

"[Kohl's] is one of the few department chains not closing stores, they're operationally focused, and they have a broad swath of stores with potentially a little extra space now," Hogan told CNBC.

Kohl's laid out plans earlier this year to whittle its square footage over time, but that doesn't entail shuttering stores altogether. Chief Executive Mansell has said that trading in some of Kohl's larger stores for pint-size locations would help the company maintain its presence in different markets and operate more profitably.

Should Kohl's hold on to some of its bigger boxes — even as it trims back excess inventory — the leftover floor space could become a "testing ground" for Amazon's next private-label fashion line, Hogan added. "We could potentially see new Amazon lines popping up in Kohl's."

Kohl's incoming CEO said she wants to take things slow. "For now, let's walk before we run," Gass told CNBC when asked about the retailer's future with Amazon.

From an operational standpoint, Kohl's has already shown it's keen to making upgrades within its stores ahead of Wednesday's launches in Los Angeles and Chicago. A new small-format location in Cincinnati, for example, features a centralized checkout near the store's entrance — placing shoppers in a single line ahead of registers — along with a redesigned kiosk for online ordering.

Kohl's shares have fallen roughly 12 percent since the start of the year, but that's a far cry from the declines logged by some of its peers, like Macy's, which has seen its stock sink more than 44 percent over the same period.

"Kohl's struggles like all department stores, but I would certainly say they've moved forward from where they were a year ago," GlobalData Retail managing director Neil Saunders told CNBC. "They're trying to drive customer traffic to stores, and the Amazon deal is the latest example of that."

Kohl's has been testing other new initiatives, like entering a partnership with Under Armour to sell the sports apparel company's merchandise. Management said on a conference call in August that it's beginning to see benefits from inventory management and cost-cutting efforts.

"Under Armour in particular continued a very strong performance and beat the sales plan across almost all categories," Mansell told analysts and investors. "We've gained significant share in active apparel and footwear in the first half of the year and expect that to continue in the back half based on assortment improvements and our momentum."

The problem for Kohl's still, according to Saunders, is that the retailer's brand image "isn't as powerful as it should be." When asked what Kohl's stands for, he said, most U.S. shoppers would likely pause and say: "I'm not actually sure."

These are the first 10 Kohl's stores, out of 82, to handle Amazon returns: